=Paper=
{{Paper
|id=Vol-2105/10000151
|storemode=property
|title=GIS Based Model of Quotas Regulation and its Impact on the
Extraction of Ecosystems’ Natural Resources and Social Welfare
|pdfUrl=https://ceur-ws.org/Vol-2105/10000151.pdf
|volume=Vol-2105
|authors=Vitaliy Kobets,Anastasiia Bystriantseva,Iryna Shakhman
|dblpUrl=https://dblp.org/rec/conf/icteri/KobetsBS18
}}
==GIS Based Model of Quotas Regulation and its Impact on the
Extraction of Ecosystems’ Natural Resources and Social Welfare==
https://ceur-ws.org/Vol-2105/10000151.pdf
GIS Based Model of Quotas Regulation and its Impact
on the Extraction of Ecosystems’ Natural Resources and
Social Welfare
Vitaliy Kobets1, Anastasiia Bystriantseva1 and Iryna Shakhman2
1
Kherson State University, 27 Universitetska st., Kherson, 73000 Ukraine
vkobets@kse.org.ua, abystryantseva@ksu.ks.ua
2
Kherson State Agricultural University, 23 Stretenskaya st., Kherson, 73000 Ukraine
shakhman.i.a@gmail.com
Abstract. Research goal of the paper is to study ecosystem using Geographical
Information System (GIS) based technology to develop valid recommendations
for sand extraction from water body. Our subject of research is GIS Based
Model of Quotas Regulation and its Impact on the Extraction of Ecosystems’
Natural Resources and Social Welfare. We used such methods as optimization
methods, GIS methods, differential-equations method, marginal benefit-cost
analysis. An example of mathematical model for determining of ecological
equilibrium during sand extracting in the ecosystem is developed using Google
Maps. The influence of economic activity due to sand extraction on fish fauna
is described. The GIS based ecological-economic model is developed on the
logistic model basis for establishing regional quotas for extraction of natural
resources during economic activity in the southern Ukraine. Regulatory
economic mechanism of natural environment is proposed. It implies such quota
for sand extraction from water body, which does not lead to deterioration of the
natural environment and stimulate the increase in social welfare.
Keywords: GIS technology, ecosystem, quota regulation, externality
1 Introduction
The surrounding world can be divided into three components: nature, human society
and economics. Humanity provides its livelihood by developing an economy, which,
in turn, functions through the consumption of tangible and intangible resources,
creating negative and positive external effects. Improvement of humanity`s well-
being should not occur due to excessive consumption of non-renewable natural
resources, but through the creation of incentives for the population to create their
needs in accordance with available natural resources, which is proclaimed the main
idea of the balanced development of world society by the United Nations. There is a
new function of the state – ecological, which is aimed to harmonize the interests of
society and nature, ensure optimal consideration of economic and environmental
interests by means of GIS. Implementation of the economic mechanism of nature
management implies such a load of economic activity, which does not lead to
undesirable consequences in biota and does not lead to deterioration of the quality of
the environment.
It is possible to follow the changes in ecological balance, the reaction of
individuals and the entire ecosystem community, expanded in time and space, with
the help of mathematical research methods. Today there is a wide range of
applications of mathematical modeling to solve many ecological and economic
problems. Moreover, the experience of using mathematical modeling does not raise
any doubts concerning the efficiency of this method in the study and forecasting the
natural ecosystems state under conditions of anthropogenic influence [1].
Local minerals (sapropel, gypsum, limestone, chalk, sand, loam, sandstone) belong
to non-renewable natural resources, the geological rate of formation or accumulation
of which is much less than the rate of human consumption. Demand for sand is
increasing in many parts of the world due to rapid economic development and
subsequent growth of building activities. Sand is considered a cheap resource,
because businesses need to cover only the exploitation cost (costs of equipment,
labor, fuel, and transport) [2]. Lack of adequate information on the environmental
impact of river sand mining is a major gap, challenging regulatory efforts in many
developing countries including Ukraine. Thus, a scientific assessment is a
precondition in setting management strategies in the sand mining areas.
Environmental impact assessment (EIA) demonstrates that the activities associated
with mining and sand processing have not only affected the health of the river
ecosystems but also degraded its overbank areas to a large extent [3].
The environmental effects of indiscriminate sand mining (for example, the annual
catchment areas of the Vembanad lake, southwest coast of India) are considered by
Padmalal D. et al [4]. The quantitative estimation of the sand mining impacts on the
rate of water level reduction in the riverbed of the catchment areas of the Vembanad
lake. Also rivers on the southwest coast of India are under immense pressure due to
indiscriminate extraction of construction grade sand, which is the most disastrous
process. The volume of in-stream mining is about 40 times higher than the sand input
estimated in the gauging stations. As a result of indiscriminate sand mining, the
riverbed in the storage zone is getting lowered at a rate of 7–15 cm. This imposes
severe damage to the physical and biological environments of these river systems [5].
In-stream mineral mining is strongly regulated in countries such as Portugal, Italy,
and New Zealand and is prohibited in countries such as France, the Netherlands
England, Germany, and Switzerland.
We proposed regulatory strategies for the overall improvement of the rivers and its
biophysical environment. The policy recommendations grounded in our the paper are
intended as guidance to decision makers in charge of sand mining to make more
informed decisions. Physical processes and biological data were collected from {data
source} to analyze optimal level of sand mining regarding damage to fish and local
biota. Our task is to minimize environmental effects which mitigate negative
consequences for both environment and social welfare. Present study examines the
impact of sand extraction on local ecology in the study area using Google Map and
Google Earth as GIS techniques. Images captured by Google Map and Google Earth
during 2017 have been used for the analysis.
The purpose of the paper is a study of ecosystem using GIS based technology to
develop valid recommendations for sand extraction from water body.
The paper is organized as follows: part 2 describes related works, part 3
demonstrates ecosystem quota model; part 4 demonstrates experimental result; the
last part concludes.
2 Related works
The study by Izougarhane M. et al [6] provided a qualitative and quantitative
assessment of the fishery's effectiveness at the mouth of the Sebou River (Morocco)
and assessment of its environmental condition. The results of the observation since
2005 and until 2016 show reduction of qualitative and quantitative indicators of
fishing. In addition, it is noted that during this period there was a change in the
physical characteristics of the water body, and the quality of water in the aquatic
environment is assessed as contaminated and very contaminated. The author notes
that the main cause of degradation of water body biodiversity is dredging.
Sowunmi F. A. et al [7] revealed significant differences from the average silt
charge of river water and quantity of fish caught by fishermen during working hours
in areas with dredging and without it. Low productivity in places of dredging works is
due to their negative impact on the environment. In areas where there were no sand
dredging works, fishermen received more extraction per day. The authors note, the
need to control the activities of sand dredges in fishing communities is to ensure the
sustainability of the environment,on one hand,, and the conservation of fishing in the
study area on the other
The interesting results are found in works of Adesina T. K., Adunola O. A. [8].
The expected effects of dredging activities on fishing of artisanal fishermen are
considered in Lagos State, Nigeria. Results of statistical studies revealed the
significant relationship between the impact of sand dredging effect on fishing
activities, the relationship between monthly income and perceived effects of sand
dredging on fishing activities. Scientists have suggested enhancing the artisanal
fishery contribution to total Gross Domestic Product (GDP), employment generation
and total increase of domestic fish production.
Akankali J. A., Idongesit A. S., Akpan P. E. [9] have assessed the physicochemical
parameters of water samples collected from upstream and downstream of OkoroNsit
(Nigeria) stream for sand mining activities: hydrogen index (ph), temperature,
turbidity, dissolved oxygen, biological oxygen demand, sulfate, nitrate, phosphate,
suspended solid, calcium, magnesium, oils and grease. It was found that river water
was polluted as a production result of sand mining activities at IsoEsuk River,
IkotAkpaEkpu. The results of some analyzed parameters of investigated substances
were within the limits of maximum permissible values, but some physical and
chemical parameters and heavy metal content were higher than the permissible water
quality standards.
Wilber D. H., Clarke D. G. [10] conducted the assessment of the biological effects
of increased concentrations of suspended sediment caused by human activities, such
as navigation dredging, on estuarine fish and shellfish. Researchers emphasize the
need for managers to determine the volume of sand extraction based on the
assessment of potential consequences of production activities during dredging.
Kim C. S., Lim H. S. discovered the prevalence and accumulation of sediment in
construction grade marine sand in the coastal waters of Korea on the basis of a
combined approach to observations and modeling [11]. Scientists used field
measurements collected during mining operations in Kyunggi Bay, Korea to develop
sediment parameters and source conditions for a three-dimensional (3D) sediment
transport model built on the Regional Ocean Modeling System (ROMS). The model is
run with realistic forcing obtained from a 9 km meteorological model, tides, and river
discharges. The resulting picture of the distribution of silt charge in depth and in
space corresponds to the data of field observations and demonstrates the character of
distribution in accordance with the granulometric composition of the sand.
Environmental problems occur when the rate of sand extraction, gravel and other
materials exceeds the rate at which natural processes generate these materials. Sand
extraction destroys the cycle of ecosystems, impacts on the biological resources
including destruction of infauna, epifauna, and some benthic fishes and alteration of
the available substrate. This process can also destroy riverine vegetation, cause
erosion, pollute water sources and reduce fish diversity. This study aims to investigate
both the positive and negative impacts of sand mining: positive in terms of financial
gain or social welfare and negative in terms of environmental impacts associated with
potential sand mining operations: and develop the best management practices in order
to minimize the adverse environmental impacts [12].
Consequently, the results of the research of world scientists proved the necessity in
development of advisory and substantiated recommendations that can be obtained by
using mathematical models. It is possible with using of system analysis, computer
modeling to investigate more deeply the mechanism of transformation of water
objects within the framework of water management works, to make plausible
scenarios of the possible development of the consequences of the impact of human
economic activity on the state of water resources in accordance with the plans of
economic development of the regions.
Sustainability of extraction of ecosystems’ natural resources depends on precise
assessment of biomass resource, planning of cost-effective logistics and evaluation of
possible environmental implications. In this context, it is important to review the role
and applications of geo-spatial tool such as GIS for precise agro-residue resource
assessment [13]. Although most conservation efforts address the direct, local causes
of biodiversity loss, effective long-term consideration of ecosystem exploration will
require complementary efforts to reduce the upstream economic pressures, such as
demands for food, water and forest products, which ultimately drive these
downstream losses [14].
Alternative economic approaches study the economy with a multidisciplinary view,
considering paradigms of social inclusion, justice and sustainability. Geographic
information science (GIScience) can be defined as a multidisciplinary and a
multiparadigmatic field, where "spatial thinking" is fundamental. The study of
environmental quality of life can be supported by the calculation of spatial
indicators [15].
The externalities produced by extraction of natural resources are multidimensional,
may strongly depend on the local context, and thus are difficult to capture through
standard environmental valuation exercises [16]. We experiment a GIS approach to
design a GIS based model of quotas regulation and its impact on the extraction of
natural resources of the ecosystem and social welfare. The set of GIS-based variables
(local context variables) prove to be significant predictors in sustainability of natural
resources of the ecosystem. We can compute simulated values that combine
information on social welfare of agents with opposite goals for use in policy choices
such as infrastructure localization and negotiation of compensations.
Changes in natural resouves are complex, thus, managing an appropriate type of
change to satisfy stakeholders with various interests is challenging. Two kinds of
conflicts might occur as a result of change in an ecosystem: (1) conflicts among
multiple ecosystem services i.e., internal conflicts and (2) conflicts among multiple
stakeholders i.e., external conflicts [17]. In our paper we develop two change
scenarios of fish recovery (net increasing and net decreasing).
Model enables decision makers to resolve internal conflicts while considering the
relative values of multiple ecosystem services to show how well the model enables
decision makers to resolve external conflicts in a group while taking into account the
diverse goals of stakeholders. Obtaining acceptable change solutions among
stakeholders with conflicting interests can lead us in moving from individual
decision-making to group-based decision-making so that we can enhance
sustainability in natural resource extracting.
Evaluation of analytical tools allows assessing the minimum amount of
information needed to properly delineate stock units. Single technical approaches are
insufficient to delineate complex fish stock structures [18]. GIS and hydro-economic
models were used in order to delineate groundwater quality zones in the Central East
of Punjab-Pakistan and observe the impact of groundwater quality on agricultural
economics [19].
Mathematical models have been widely used to simulate all aspects of bioenergy
production systems. Thus GIS-based approach is a powerful method to collect data,
perform spatial analysis, combine and manage both spatial and attributes data inside a
determinant region [20].
A GIS is used for locating the service areas of businesses and corresponding
environmental conditions. For ecological models, the results suggest that on average
there is a significant increase in efficiency of responsible decision and policy makers
about extraction of natural resources when externalities are incorporated in the
function of resources extraction. This suggests that businesses have internalized the
effects of fishery decreasing and have adapted to the environment in which they
operate. The results can simulate decision-making in public safety issues (design of
model extraction, regulations of quotas).
We try to answer how to specifically estimate the ecological impact of sprawl of
natural resources extraction using GIS and ecological valuation method. An
ecological estimation method examines the economic losses of natural environmental.
3 Ecosystem Model of Quotas Regulation
Mechanisms responsible for the development of the natural system can be determined
with consideration of the functioning of the biological or ecological system as the
result of the interaction of their constituent and external factors. It is reflected in the
change of the environment state in which these systems are considered. It is possible
to thoroughly investigate the interaction of various factors through the use of
mathematical methods and methods of mathematical modeling. These mathematical
and simulation models can be used to test various scenarios and strategies in order to
minimize ecological effects. We can charge specific quotas for sand exploitation
using benefit-cost analysis, where benefit is a profit of businesses which extract sand;
cost is a decreasing of fish population in monetary terms.
In the decision-making concerning the sand extraction, in particular sand and gravel
material [21], the apparatus of game theory (GT) can be used. When studying and
analyzing conflict issues and trying to predict the behavior of competitive players, GT
approaches allow simulation of the self-centred attitude of the involved players with a
fairly realistic manner. In that context, GT methods compared to other conventional
methods of strategic analysis, such as linear programming, make better estimates of
the game outcome. The role of GT is to propose a methodology about good
governance of the mining sector that promotes a sustainable sharing of aggregate
resource by securing environment and safekeeping revenues in mining trade market.
The simplest case of controlling the dynamics of a ecosystem’s population is
realized when the population’s change rate is proportional to the deviation from its
equilibrium state (Malthus model):
dN
= k ⋅ ( N − N0 ) (1)
dt
Here fish population grows proportionally to their available quantity. The solution
of the equation has the form: N = N 0 + ( N1 − N 0 ) ⋅ e kt , where N1 is a deviation from
the equilibrium state at time t = 0 . For k > 0 , the ecosystem will deviate from the
equilibrium state N 0 , whereas for k ≤ 0 the system will return to its equilibrium
state. The encroaching speed or removal speed will depend on the absolute value of
the control parameter k . Linear models are aimed to maintain the system in its
current state, whereas in the ecosystem it is often necessary to transfer the system
from one state to another, which is more desirable according to certain criteria.
Nonlinear models allow the system to be moved from one state to another.
Population dynamics can be adequately described by means of one independent
variable quantities, and factors influencing the state of the system are taken into
account in the form of given constants. One of the nonlinear models that allows this to
be done is a logistic model that takes the form of the following equation:
dN * N*
= aN * 1 − * (2)
dt K
where N * (t ) – number of population at the moment of time t , a – Malthusian
parameter, K * – ecological carrying capacity [22].
During the sand extraction, a temporary effect on the fish fauna is expected. It is
manifested by the death of baby fish and fodder organisms, due to the increase of silt
charge in surface waters from dredging. Dredgers form zones with significant
quantities of silt charge. In addition, during soil removal, hydrobiota can suffocate
and die. In the zone of high turbidity it is necessary to take into account the influence
of silt charge both in the water column and on the bottom, which is especially
important for spawning grounds and feeding places for young fish.
The reaction of fish during sand mining (response of biota to anthropogenic impact)
manifests itself by the removal of adult individuals outside the zone of impact of the
dredger immediately after the sensation of noise and vibration. Baby fish that are not
yet capable to move by themselves, and caviar from the bottom and the water column
will die in accordance with the increase in turbidity, that is, under the condition of
continuous operation of the dugout for a long time. This may be in line with the
condition of exceeding birth-rate mortality (negative ‘a’).
The inhibition of the fish fauna in the area of sand extraction has a local and
temporary character and, after a while, there will be processes of natural reclamation
of the organisms of the bottom fauna. Restoring of the feed base after the completion
of the sand extraction is carried out for a certain time. Then the adult fish will return
(some species of fish, even with certain indicators of turbidity), and the birth rate will
eventually recover.
The equation (2) is integrated by the division of variables, and its solution
determines the number of population at the moment of time t , has the form:
K * N 0 e at
N* = *
( )
K + N 0 e at − 1
(3)
where N 0 – initial number of fish in a water body.
The Ferkhyulst model is a generalization of Malthus model for existing restrictions
on the extraction of natural resources. In this case, the management of the quotas for a
sand extraction should be made in such a way as to achieve the maximum profit from
the extraction of this sand, under condition that it is preserved for future use, and this
extraction should not exhaust the catch of fish in the water body. Alternative
management models may include sand extraction at constant speed c in the form
dN * N*
= aN * 1 − * − с or quota may be determined in proportion to the available
dt K
dN * N*
quantity of sand: = aN * 1 − * − p ⋅ x , where p is a speed of sand
dt K
extraction [23]. Alternative models require daily monitoring by GIS technology,
while the Ferkhyulst model allows setting a quota based on available monitoring data
using GIS.
If it becomes necessary to simulate the ecosystem or its individual components
under variable in time external conditions, then the problem is reduced to the
consideration of a non-autonomous system. At first, an autonomous system (model) is
built and studied [1].
In accordance with the methodology for calculating damage [24], which is caused
to the fish industry due to soil extraction, works, damage to the caviar, larvae and
baby fish by hydraulic dredger is determined by the formula:
K
N = ПVR M. (4)
100
where N – amount of damages, П – number of caviar, larvae and baby fish, V –
volume of extracted soil, R – multiplicity of soil dilution with water, K – coefficient
of industrial return from caviar, M – average weight of the adult fish.
If we need to determine the population size (caviar, larvae and baby fish), which is
large enough, it is more convenient to use non-deterministic, but continuous models
that have an independent variable of time. In the absence of other independent
variables, it is described by ordinary differential equations.
Accepting that from equalities (3), (4), we get:
K * N 0 e at K
N= * ⋅ VR M.
K + N 0 ( e − 1)
at
100
After separating independent of t values we get:
K V ( t ) eat
N ( t ) = K * N 0 RM ⋅ * .
100 K + N 0 ( e at − 1)
(5)
The resulting equation (5) is a dependence that describes an autonomous system.
One of the important properties of an autonomous system (model) is that it can
have stationary solutions that determine the state of equilibrium of the real ecological
system. It is necessary to find points that correspond to the state of equilibrium of the
autonomous system (model). In the state of equilibrium, all the indicators of the
ecosystem do not change over time, so in the stationary state, all derivatives of time in
dN
the system are zero, that is = 0:
dt
dN K dt
( )
e + aVe at K * + N 0 ( e at − 1) − Ve at ⋅ N 0 ae at
dV at
= K * N 0 RM ⋅ .
(
K * + N ( eat − 1) )
2
dt 100
0
= 0 , K * + N 0 ( e at − 1) ≠ 0 , then
dN
As
dt
dV at
e + aVe at ( K * + N 0 eat − N 0 ) − aVN 0 e 2 at = 0 ;
dt
e ( K + N 0 e at − N 0 ) + K * aVeat + aVN 0 e 2 at − N 0 aVe at − aVN 0 e2 at = 0 ;
dV at *
dt
e ( K + N 0 eat − N 0 ) + K * aVeat − N 0 aVe at = 0 .
dV at *
dt
Taking into account e at ≠ 0 for t ∈ R , we get:
( K * + N0 eat − N 0 ) dV
dt
+ ( K * a − N0 a )V = 0 .
As a result of finding the derivative (5) and equating the result to zero, we obtain
dV
the differential equation :
dt
( K * − N0 + N0 eat ) dVdt
= a ( N 0 − K * )V . (6)
The equation (6) is integrated by the division of variables:
N − K*
dt , ln V = a ( N 0 − K * ) ∫ *
dV dt
= a⋅ * 0
V K − N0 + N0e at
K − N 0 + N 0 e at
ln V = a ( N 0 − K * ) * ( )
t 1
− ln K *
− N + N e at
,
K − N0 a ( K * − N0 ) 0 0
ln V = −at + ln ( K * − N 0 + N 0 e at ) ,
V = ( K * − N 0 + N 0 e at ) e − at .
The solution of the equation, which determines the volume of extracted sand at the
moment of time t , has the form:
K * + N 0 ( e at − 1)
V (t ) = . (7)
e at
4 GIS Based Approach and Quota Setting Experiment for Fish
Population
4.1 GIS Based Approach
There is an acute need for regulation of production activities for the extraction of
natural resources, calculation and allocation of quotas, depending on the ecological
and economic situation of a particular area. Since 2016 in the Kherson region the
solution of these problems requires conducting of hydrogeological survey,
implementation of basin water management schemes, in particular in the Dniprovsky
Basin Water Resources Management, substantiation of maximum allowable water and
ecological loads, introduction of water management ecological-economic models. The
data as a result of such works is extremely necessary for establishing regional quotas
for extraction of natural resources while solving economic issues of southern Ukraine.
Representatives of local authorities and public organizations are concerned about
the illegal sand extraction on the territory of the Kakhovka Reservoir. Thus, in the
village Vesele, the Beryslav region, illegal sandwash and export of sand from the
territory of the Kherson region are taking place (carts and barges go to Kamianske) as
we can estimate from Google Map (fig.1).
Over the last decade or more, geographic information systems (GIS) have proved to
be agile and powerful tools in academic and applied fields. The Google Maps mashup
as Web application exhibits great potential to be a real live GIS. The power of GIS to
analyze and illustrate suggested that public access to planning processes and research
of many types would be greatly enhanced. Google Maps is a service which portends a
subtle shift in GIS and what much of the world will be expecting of online geospatial
business in coming years. Google Maps, the official Web service, is a quite simple
tool very much similar to other online mapping services like MapQuest, Yahoo! Maps
etc. This is a staple of Web-based GIS, and in Google Maps it is limited to only three
choices: digital orthophotos, symbolized street maps, and a hybrid of the two [25].
Fig. 1. Google Map based screenshot as GIS of sand extraction on the territory of the
Kakhovka Reservoir
When one of results plotted on the map is clicked, a small scale is demonstrated in
the bottom of this box. There is a unique and important additional component of
Google Maps – its mashability. Google Maps mashups are the resultant combinations
of the existing Google Maps geospatial query/display engine with geospatial data
provided by non-Google users [25]. Google Maps lacks analytical power and
accuracy, but it can be a platform for the addition of value by a participating public, a
service to be mashed up, and the system to be possibly revised. It helps to build
geospatial information resources that answer specific needs of specific industries.
It means creation of public participation geographic information system (PPGIS)
that could support include necessary data to process information and make decisions
of responsible persons. PPGIS applications have been extensive, ranging from
community and neighborhood planning to environmental and natural resource
management to mapping traditional ecological knowledge of people [26]. Example of
Google Map application is demonstrated in table 1.
Table 1. Google Map applications
Year Implementation mode Location
2011 Google Maps Otago Region (New Zealand)
2011 Google Maps Southland Region (New Zealand)
2011 Google Maps South West Victoria (Australia)
2010 Google Maps Kangaroo Island (South Australia)
2010 Google Maps Grand County (Colorado, U.S.)
In a recent Web-based PPGIS application authors provided an integrated Google
Maps and Google Earth application interface that allowed participants the opportunity
to examine and map any attribute in investigated area. We can distinguish 4 methods
for collecting spatial information via PPGIS: 1) paper map and markers; 2) paper map
and sticker dots; 3) flash-based Internet applications; 4) Google Maps/Earth Internet
application [26]. Therefore we need to augment these applications with statistical data
to make more a informative decision about resource extraction.
On the other hand authors [27] do not include popular web mapping Application
Programming Interfaces (API’s), such as Google Maps, Yahoo! Maps or BingMaps,
Google Earth application on the list of free and open sources (fig. 2).
Fig. 2. Free and open source GIS Software
The reason is, that these maps are only free-of-charge in certain situations, and that
their licence agreement imposes restrictions on users that limit the APIs uses to
certain types of applications. For example these APIs are not free for commercial use,
and private users are restricted in the daily frequency of use (number of map requests)
of the services offered through these API. A recent example for a license change is
the Google Maps API [27].
4.2 Quota Setting Experiment for Fish Population
Assume that a fish population at time t varies according to the following differential
equation:
dN N
= aN 1 − (8)
dt K
where K – maximum capacity of fish in a water body, N – number of fish at time
t , parameter a > 0 . The solution of equation (8) is determined by the following
logistic curve (fig. 3). The dynamics of the fish population is described by the logistic
curve in fig. 3.
Fig. 3. The dynamics of the fish population (horizontal axis is time period in months, vertical
axis is a number of fish population in tons)
In order to conduct a study, we need to choose the location of the site that is
planned to be used for the sand extraction, taking into account the possible influence
on the hydraulic structures that are below the current from the place of the sand
extraction (Kakhovka HPS). The size of the production site, from which area sand is
extracted, is determined by taking into account the relief of the water body and the
coastal strip, the capacity of the sand deposits and the technical characteristics of the
used equipment. Conditional unit of sand extraction taking into account the received
values of quotas (20 tons), can be obtained from the area of 1 km2 and, for example,
corresponds to a strip along a coastline with a width of 0.05 km and a length of
20 km.
Let’s set the following parameters for a water body, where sand is extracted from,
for example, for building on the basis of quotas established by the regulatory
authorities. The net growth rate of freshwater fish is 5% per year. The volume of
water and sand are determined using GIS technology: the maximum sand capacity is
V = 1000 tons, max K = 20 . The losses from the sand extraction in a water body are
calculated by the formula:
K
N = N *VR M (9)
100
Indices of equation (9) are explained in table 2.
For the initial values of the parameters, we will determine the social welfare SW ,
taking into account the profit of the business Π , which extracts sand from the water
body and losses from loss of fish c ⋅ N (negative externality) due to the sand
extraction. The volume of sand extraction is determined by the formula (7).
Table 2. Initial parameters for the calculation of losses from the sand extraction
Explanation of the
Parameters Units of measurement
parameters
amount of fish population’s
N Kg
loss
number of fish in a animal unit
N* population at time t m3
V volume of sand extraction m3
multiplicity of soil dilution
R with water
-
coefficient of industrial
K return from caviar
-
M average weight of the adult Kg
The dynamics of extracted sand volume V (m3) for discrete time intervals
(months) is shown in Table 3. The total revenue of the sand owner is calculated by the
formula TR = P ⋅ V ( P – price per 1 m3). The profit of a firm that extracts sand is
Π = TR − TC . The population of the fish at time t is determined from the formula (9)
and is presented in table 3. Amount of fish population loss N is calculated by the
formula (3), and the number of fish in the population N * is computed by the formula
(2) in table 3. In the monetary equivalent, the losses from damage done to fish
(negative externality) due to sand extraction equal c ⋅ N . Social welfare (net gain or
V
loss of society) SW = Π − c ⋅ N . Quota is Q = .
max V
Table 3. Dynamics of ecosystem's indicators due to sand extraction
t V TR TC П N* N c⋅N SW Quota
0 20 16800 12600 4200 10 70 3150 1050 2,0%
1 19,51 16390,33 12292,75 4097,58 10,25 70,00 3150 947,58 2,0%
2 19,05 16000,63 12000,48 4000,16 10,50 70,00 3150 850,16 1,9%
3 18,61 15629,95 11722,46 3907,49 10,75 70,00 3150 757,49 1,9%
4 18,19 15277,34 11458,00 3819,33 11,00 70,00 3150 669,33 1,8%
5 17,79 14941,93 11206,44 3735,48 11,24 70,00 3150 585,48 1,8%
6 17,41 14622,87 10967,15 3655,72 11,49 70,00 3150 505,72 1,7%
7 17,05 14319,38 10739,53 3579,84 11,73 70,00 3150 429,84 1,7%
8 16,70 14030,69 10523,02 3507,67 11,97 70,00 3150 357,67 1,7%
9 16,38 13756,08 10317,06 3439,02 12,21 70,00 3150 289,02 1,6%
10 16,07 13494,86 10121,14 3373,71 12,45 70,00 3150 223,71 1,6%
11 15,77 13246,38 9934,78 3311,59 12,68 70,00 3150 161,59 1,6%
12 15,49 13010,02 9757,51 3252,50 12,91 70,00 3150 102,50 1,5%
13 15,22 12785,18 9588,89 3196,30 13,14 70,00 3150 46,30 1,5%
14 14,97 12571,32 9428,49 3142,83 13,36 70,00 3150 -7,17 1,5%
15 14,72 12367,88 9275,91 3091,97 13,58 70,00 3150 -58,03 1,5%
The task of the regulator is to determine the quota at which social welfare will
remain positive. In table 3 the quota size will be 1.5%. With a given quota size, the
number of periods for granting a license on the sand extraction should be no more
than 14 periods (months). The dynamics of social welfare is demonstrated in fig. 4,
where during transition from 14 to 15 periods (initial first period is indicated as «0»),
the increase in social welfare modifies from positive to negative meaning.
Fig. 4. Dynamics of social welfare due to sand extraction from water body (horizontal
axis is time period in months, vertical axis is social welfare in monetary units)
5 Conclusions and Outlook
Instream mining can be conducted without creating adverse environmental impacts
provided that the mining activities are kept within the limited optimal volume of sand
mining set by the local authorities.
An example of mathematical model for determining of ecological equilibrium
during sand extracting in the ecosystem is developed using Google Maps. The
influence of economic activity due to sand extraction on fish fauna is described. The
GIS based ecological-economic model is developed on the logistic model basis for
establishing regional quotas for extraction of natural resources during economic
activity in the southern Ukraine. Regulatory economic mechanism of natural
environment is proposed. It implies such quota for sand extraction from water body,
which does not lead to deterioration of the quality of the natural environment and
stimulates the increase in social welfare.
We demonstrated that for chosen quota size, the number of periods for granting a
license for the sand extraction should be no more than 14 periods (months) for our
experiment in the Kherson region (Ukraine) using real data. The data of such works is
extremely necessary for establishing regional quotas for extraction of natural
resources in solving economic issues of southern Ukraine. This dynamic approach
gives possibility to expand these results for local and national authority to determine
quota size which saves exhaustible natural resources and increases social welfare for
all participants using GIS based technologies.
References
1. Lavryk V.I.: Methods of mathematical modeling in ecology. Vydavnychyi dim KM
Akademiia, Kyiv (2002).
2. Gavriletea, M.D.: Environmental Impacts of Sand Exploitation. Analysis of Sand Market.
Sustainability 9, 1--26 (2017) doi:10.3390/su9071118.
3. Sreebha, S., Padmalal D.: Environmental Impact Assessment of Sand Mining from the
Small Catchment Rivers in the Southwestern Coast of India: A Case Study. Environmental
Management 47(1), 130--140 (2011) doi:10.1007/s00267-010-9571-6.
4. Padmalal, D.: Environmental effects of river sand mining: a case from the river
catchments of Vembanadlake, Southwest coast of India. Environmental geology 54(4),
879--889 (2008).
5. Padmalal, D., Maya, K., Sreebha, S., Sreeja, R.: Environmental Effects of River Sand
Mining: A Case From the River Catchments of Vembanad Lake, Southwest Coast of
India. Environmental Geology 54(4), 87--889 (2008) doi:10.1007/s00254-007-0870-z.
6. Izougarhane, M.: Impact of sand dredging on the coastal and artisanal fishing in estuary
Sebou (Morocco). Biolife 4 (4), 661--667 (2016).
7. Sowunmi, F. A.: Economic Burden of Sand Dredging on Artisanal Fishing in Lagos State,
Nigeria. Poult Fish Wildl Sci 171 (4), 1--8 (2016).
8. Adesina, T.K., Adunola, O.A.: Perceived Effects of Sand Dredging on Livelihood
Diversification of Artisanal Fisher Folks in Lagos State, Nigeria. Agricultura Tropica et
Subtropica 50 (2), 71--79 (2017).
9. Akankali, J.A., Idongesit, A.S., Akpan, P.E.: Effects of sand mining activities on water
quality of OkoroNsit stream, NsitAtai local government area, AkwaIbom state, Nigeria.
International Journal of Development and Sustainability 6(7), 451--462 (2017).
10. Wilber, D.H., Clarke, D.G.: Biological effects of suspended sediments: a review of
suspended sediment impacts on fish and shellfish with relation to dredging activities in
estuarie. North American Journal of Fisheries Management 21(4), 855--875 (2001).
11. Kim, C.S., Lim, H. S.: Sediment dispersal and deposition due to sand mining in the coastal
waters of Korea. Continental Shelf Research 29(1), 194--204 (2009).
12. Ashraf, M.A., Maah, M.J., Yusoff, I., Wajid, A., Mahmood, K. Sand Mining Effects,
Causes and Concerns: A Case Study from Bestari Jaya, Selangor, Peninsular Malaysia.
Scientific Research and Essays 6 (6): 1216--1231 (2011) doi:10.5897/SRE10.690.
13. Hiloidhari, M.: Emerging role of Geographical Information System (GIS), Life Cycle
Assessment (LCA) and spatial LCA (GIS-LCA) in sustainable bioenergy planning.
Bioresource technology, 242, 218--226 (2017).
14. Kitzes, J.: Consumption-Based Conservation Targeting: Linking Biodiversity Loss to
Upstream Demand through a Global Wildlife Footprint. Conservation letters, 10(5), 531--
538 (2017).
15. Cabrera-Barona, P.: From The 'Good Living' to The 'Common Good': What is the role of
GIScience? Joint Urban Remote Sensing Event 2, 1--4 (2017).
16. Giaccaria, S., Frontuto, V., Dalmazzone, S.: Valuing externalities from energy
infrastructures through stated preferences: a geographically stratified sampling approach.
Applied Economics 48, 5497--5512 (2016).
17. Tayyebi, A. et al.: Group-based crop change planning: Application of SmartScape (TM)
spatial decision support system for resolving conflicts. Ecological modeling 333, 92--100
(2016).
18. Pita, A. et al.: Conceptual and practical advances in fish stock delineation Preface.
Fisheries research 173, 185--193 (2016).
19. Shakoor, A. et al.: GIS based assessment and delineation of groundwater quality zones and
its impact on agricultural productivity. Pakistan journal of agricultural sciences 52 (3),
837--843 (2015)
20. Widaningrum, D.L.: A GIS - Based Approach for Catchment Area Analysis of
Convenience Store, In: 3rd Information Systems International Conference, pp. 511-518.
Surabaya, Procedia Computer Science (2015).
21. Podimata, M.V., Yannopoulos P.C.: A conceptual approach to model sand –gravel
extraction from rivers based on a game theory perspective. Journal of Environmental
Planning and Management 59 (1), 120--141 (2016), doi: 10.1080/09640568.2014.991381.
22. Kobets, V., Yatsenko, V. Adjusting business processes by the means of an autoregressive
model using BPMN 2.0 (2016), CEUR Workshop Proceedings, vol. 1614, P. 518-533
(Indexed by: Sci Verse Scopus, DBLP, Google Scholar). Available: CEUR-WS.org/Vol-
1614/ICTERI-2016-CEUR-WS-Volume.pdf
23. Shiyan, A.A.: Economic Cybernetics: Introduction to Social and Economic Systems
Modeling. Magnolia, Lviv (2007).
24. On Approval of the Methodology for calculation of damages caused by the fish farming as
a result of violation of the legislation on the protection of the environment. Mode of
access: http://zakon0.rada.gov.ua/laws/show/z0155-95.
25. Miller, C.C.: A Beast in the Field: The Google Maps Mashup as GIS/2. Cartographica:
The International Journal for Geographic Information and Geovisualization 41 (3), 187--
199 (2006) doi:10.3138/J0L0-5301-2262-N779.
26. Brown, G.: Public Participation GIS (PPGIS) for regional and environmental planning:
reflections on a decade of empirical research. Journal of Urban and Regional Information
Systems Association 25, 7--12 (2012).
27. Steiniger, S., Hunter, A.: The 2012 free and open source GIS software map – A guide to
facilitate research, development, and adoption. Computers, Environment and Urban
Systems 39, 136--150 (2013).